What is electric field?

Question

What is electric field in real? Any theory?

We generally think it as a mathematical construct but it's a real quantity. So what is the nature of that quantity.

Answer 1

It is a elementary field of nature. We can describe it as a component of the electromagnetic field that includes also the magnetic field. Under the current experimental evidence, we cannot explain the electromagnetic field in terms of anything more fundamental.

Answer 2

An electric field is the "reach" of an electric charge.

Why fields exist, we can't explain. We can only measure that they exist and investigate how they work.

It may seem puzzling and maybe unimaginable and unintuitive. But it's not much different from, say, the very well-know gravitational field (except for the sign - gravity can only attract not repel, but that's besides the point):

You fall down towards Earth due to gravity. If you go to the other side of Earth, then you are still pulled towards the centre of Earth. The higher up you come, the weaker gravity is. This means that at every point around the Earth, there is a certain gravitational pull in you, in your mass. To standardize it you might ask how large this pull is per unit mass, so: gravitational force per kilogram.

This is a field. A gravitational field in this case. It extends into empty space and travels through no medium. We define it on a per-unit base to keep it standardized. An electric field is exactly the same, just caused by another source: whereas gravitational fields spring from mass, electric fields spring from electric charges. An electric field is thus: electric force per unit charge at any given point.

It is hard to explain why these masses and charges cause fields around them. Physics is rarely able to explain "why" questions at the fundamental level. Nevertheless, if you intuitively accept the explanation of gravity, then it should be no issue to likewise accept electric fields.